Falking is a term used to refer to unknown and persistant stalking by individuals on Facebook.

Gill: "hey I went on a date with that girl I met on eHarmonyJohn: "Isn't that the hot girl that you friended last week on Facebook?"

Gill: "sort of. We're not friends, I'm was Falking her before our date . She gave me her email address and I used Gmail to get her last name. I had to track her down, to make sure she was cool before the date"
John: "so, how was the date?"
Gill: Ah . . .not so good, I'll just keep "Falking" her until she updates her security on Facebook, her pics are pretty hot.